A new theoretical approach is developed for remote temperature sensing based on Laplace transform techniques applied to the radiative transfer equation. This approach allows calculation of the atmospheric temperature profile based on measurements of the upwelling radiance and its derivatives. A detailed numerical study of this technique is carried out and the technique is applied to measurements of the upwelling radiance taken with a balloon-borne Fourier transform spectrometer (SCRIBE), and to data from the Tiros Operational Vertical Sounder (TOVS). Limitations of the technique arising from experimental errors, truncation errors, roundoff errors, and other causes are discussed. Keywords: Differential inversion; Remote sensing; Atmospheric temperature profiles.